Reproducing Kernel Hilbert Space vs. Frame Estimates

Palle E. T. Jorgensen and Myung-Sin Song
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Palle E. T. Jorgensen: Department of Mathematics, The University of Iowa, 14 MacLean Hall, Iowa City, IA 52242, USA
Myung-Sin Song: Department of Mathematics and Statistics, Southern Illinois University Edwardsville, Box 1653, Edwardsville, IL 62026, USA

Mathematics, 2015, vol. 3, issue 3, 1-11

Abstract: We consider conditions on a given system F of vectors in Hilbert space H , forming a frame, which turn H into a reproducing kernel Hilbert space. It is assumed that the vectors in F are functions on some set ? . We then identify conditions on these functions which automatically give H the structure of a reproducing kernel Hilbert space of functions on ?. We further give an explicit formula for the kernel, and for the corresponding isometric isomorphism. Applications are given to Hilbert spaces associated to families of Gaussian processes.

Keywords: Hilbert space; frames; reproducing kernel; Karhunen-Loève (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2015
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